Problem set 9 – Output and exchange rates in the short term

Global Economy II – Spring 2019/20 Miguel Lebre de Freitas Sharmin Sazedj

Problem set 9 – Output and exchange rates in the short term

Exercises

9.1. [Money market, AA curve]. Consider an open economy, where the price level is initially equal to the foreign price level, which is constant (PP^*1), and the nominal exchange rate is equal to 1. The interest rate is initially equal to the foreign interest rate, i*=0.1. The home money demand is given by m^D Y 10i, nominal money supply is M=100, and the economy is initially at the full employment output is Y_f 100.

a) Describe the money market equilibrium.

b) Taking into account that the money supply is expected to remain constant in the long run, find out the expected exchange rate. Use the uncovered interest parity to relate the spot exchange rate to the interest rate.

c) Using the UIRP, describe the AA curve for this economy. Explain why it is negatively sloped.

d) Examine now the effects of a temporary shift in the money supply, to M=200. In particular, describe the new AA curve.

e) Suppose now that the monetary shock was permanent. Find out the new expected future exchange rate curve, as well as the expression for the new AA curve in this case. Compare with d).

f) Departing from e), explain the adjustment of the AA curve to the long run.

9.2. [Goods market, DD curve]. Consider an open economy, where domestic and foreign goods are imperfect substitutes. Initially, the price level is equal to the foreign price level, which is constant (PP^* 1), and the nominal exchange rate is equal to 1. The components of the aggregate demand D=C+I+G+TB have the following expressions: C=10+0.5Y, I=10, G=30, TB5



1



, where  eP^* P. It is also known that full employment output is Y_f 100 and the foreign interest rate is constant and equal to i^* 10%.

a) Find out the equilibrium level of output in the short term, and describe it graphically using the Keynesian cross. Explain what would happen if the nominal exchange rate changed to e=0.5.

b) Find out the expression of the DD curve and describe it in a graph. Explain why it is positively sloped.

c) Suppose that government expenditures increase by 2.5. Describe the impact on the DD curve assuming that the shock was transitory.

d) Examine now the implications for the expected exchange rate of a permanent shift in the fiscal policy to G=32.5.

9.3. The following table displays estimated export and import price elasticities of export and of imports relative to the exchange rate, measured over three successively longer time horizons, and thus allows for the possibility that export and import demands adjust gradually to relative price changes, as in our discussion of the J-curve effect. “

Given these figures, what can you say about the slopes of the DD curve, in the short run an din the long run, in (a) Denmark; (b) France; (c) Switzerland.

9.4. [AA curve, Liquidity Trap]. Consider an open economy, where P1. The foreign interest rate is i*=0.1. The home money demand is given by

i Y

m^D 1010 , nominal money supply is M=20, and the expected exchange rate is 1.8.

a) Assume first that Y=100. Describe the money market in this case. How much will be the exchange rate? What if Y=210? [E=2; E=1,8]

b) Describe and represent in a graph the AA curve.

c) Describe the impact on the AA curve of an increase in money supply to M=40.

d) Describe the impact on the AA curve of an increase in the expected exchange rate to E(e)=3.6.

9.5. [Monetary expansion]. Consider an open economy, where aggregate demand is given by the following expression: Y 9010

 

e P . The demand for money is given by m^DY 10i, nominal money supply is M=100, the foreign price level is

constant and the foreign interest rate is equal to i*=0.1. The economy is initially at the full employment, Y_f 100, with a constant price level and a constant exchange rate.

a) Describe the initial equilibrium in the AA-DD diagram.

b) Examine, numerically and graphically, the implications of a temporary expansion in the money supply to M=200.

c) Examine, numerically and graphically, the implications of a permanent expansion in the money supply to M=200. In particular, compute (c1) the expected exchange rate; (c2) the new AA curve; (c3) the short term equilibrium; (c4) The long run AA and DD curves and the long run equilibrium.

9.6. [Fiscal expansion] Consider an open economy, where the AA curve is described by the following equation: Y 1000E

 

e e900. The goods market equilibrium is described by the following expression: ^Y2



^ATB



, where TB5

 

e1 . Initially, A 50, the economy is at full employment, Y_f 100, and no change in policy is expected.

a) Describe the initial equilibrium in the AA-DD diagram.

b) Examine, numerically and graphically, the implications of a temporary fiscal expansion, so that A'52.5.

c) Examine, numerically and graphically, the implications of a permanent fiscal expansion, so that A'52.5.

9.7. [Foreign demand shock, policy responses, liquidity trap]. Consider an open economy, with sticky prices under flexible exchange rates. The foreign interest rate is i*=0.1. The home money demand is given by m^DY 1010i, the nominal money supply is M=20, and full employment output is Y_f 210. The goods market equilibrium is described by ^{Y 4}



^ATB



^{, where} TB5



e p1.8



, and initially

5 .

52 A .

a) Assuming that the economy is initially at full employment and no changes in the exchange rate are expected, find the expressions of the AA and DD curves, as well as the initial price level and the exchange rate [1; 1.8].

b) Assume that, due to a permanent shift in the foreign demand, the equation describing the trade balance shifted to TB5



e p2.5



. Describe the adjustment of the economy to this shock, assuming no changes in policy.

Would monetary or fiscal policies help achieve the internal and external balance in this case? [e=2.5; TB=0].

c) Assume now that, instead of permanent, the shock described above was of temporary nature. Describe the short term equilibrium after the shock in this case, computing: (c1) the exchange rate; (c2) the output level; (c3) the TB [2;

200; -2.5].

d) Suppose the monetary authorities, concerned with price stability, used a temporary monetary expansion to bring the economy back to full employment.

Would that be possible? Why? [i=0].

e) Suppose instead that was up to the fiscal authorities to stabilize the output level. How should the level of autonomous spending be adjusted? Would the economy meet the external balance in the new short term equilibrium? [56; - 3.5].

f) Now suppose the monetary authorities gave away price stability, to engage in in a permanent, once-and-for-all, monetary expansion. Assuming that the policy was credible, how much should be the new money supply for the economy to meet the internal balance in the short term? Describe the implied short run equilibrium and quantify the TB in that equilibrium. Finally, describe the subsequent adjustment of this economy, and quantify the long term values of prices, exchange rate, and trade balance [25; 0, 1.25, 2.25, 0 ].

9.8. Consider an open economy with sticky prices under flexible exchange rates. In this economy, money supply is equal to M=100, money demand is given by

i Y

m^D  5 , and full employment output is Y_f 100. The interest rate parity holds instantaneously and the foreign interest rate is equal to i*=0.2. The components of the aggregate demand D=C+I+G+TB have the following expressions:

C=12.5+0.75(Y-T), I=10, G=T=10, TBX5



1



, where  e P.

a) Find out the expression of the DD curve as a function of X and . Assume first that X0 and the economy is initially at full employment. Find out the domestic price level, the nominal exchange rate, the trade balance and the government balance. [P=1, E=1, TB=0, T-G=0 ]

b) Now consider a temporary fall in foreign demand, so that (X5). Find out the implied short run equilibrium, and display it in the AA-DD diagram.

Explain what happens to the nominal exchange rate and to the trade balance.

[E=1,04; TB=-4,8]

c) Discuss, using the AA-DD schedule, and quantifying when possible, the effectiveness of temporary moves in fiscal versus monetary policy to restore full employment. [G=15]

d) Describe the automatic adjustment of the economy if the external shock (to

5



X ) was of permanent nature instead. What would happen to the nominal exchange rate, output, and to the trade balance in that case? Represent in a graph. [E=2, Y=100, TB=0]

9.9. [Fiscal expansion] Consider an open economy, where the AA curve is described by the following equation: Y200E

 

e e100. The goods market equilibrium is described by the following expression: ^{Y 5}



^ATB



, where TB4eY/5. Initially, A20, the economy is at full employment, Y_f 100, and no change in policy is expected.

e) Describe the initial equilibrium in the AA-DD diagram. [Y=100, E=5]

f) Examine, numerically and graphically, the implications of a temporary fiscal expansion, so that A'24. Analyse numerically and graphically the impact on the trade balance. [Y=108, E=4,8]

g) Examine, numerically and graphically, the implications of a permanent fiscal expansion, so that A'24. Analyse numerically and graphically the impact on the trade balance. [Y=100, E=4]